974 CHAPTER 9 Systems and Matrices 32. Concept Check Each graphing calculator screen shows A-1 for some matrix A. Find each matrix A. 1Hint: 1A-12-1 = A2 (a) (b) Concept Check Show that the matrix inverse method cannot be used to solve each system. 45. 7x - 2y = 3 14x - 4y = 1 46. x - 2y + 3z = 4 2x - 4y + 6z = 8 3x - 6y + 9z = 14 Solve each system using the inverse of the coefficient matrix. For Exercises 49–54, the inverses were found in Exercises 25–30. See Example 4. 47. x + y + z = 6 2x + 3y - z = 7 3x - y - z = 6 48. 2x + 5y + 2z = 9 4x - 7y - 3z = 7 3x - 8y - 2z = 9 49. 2x + 3y + 3z = 1 x + 4y + 3z = 0 x + 3y + 4z = -1 50. -2x + 2y + 4z = 3 -3x + 4y + 5z = 1 x + 2z = 2 51. 2x + 2y - 4z = 12 2x + 6y = 16 -3x - 3y + 5z = -20 52. 2x + 4y + 6z = 4 -x - 4y - 3z = 8 y - z = -4 53. x + y + 2w = 3 2x - y + z - w = 3 3x + 3y + 2z - 2w = 5 x + 2y + z = 3 54. x - 2y + 3z = 1 y - z + w = -1 -2x + 2y - 2z + 4w = 2 2y - 3z + w = -3 Solve each system using the inverse of the coefficient matrix. See Example 4. 33. -x + y = 1 2x - y = 1 34. x + y = 5 x - y = -1 35. 2x - y = -8 3x + y = -2 36. x + 3y = -12 2x - y = 11 37. 3x + 4y = -3 -5x + 8y = 16 38. 2x - 3y = 10 2x + 2y = 5 39. 6x + 9y = 3 -8x + 3y = 6 40. 5x - 3y = 0 10x + 6y = -4 41. 0.2x + 0.3y = -1.9 0.7x - 0.2y = 4.6 42. 0.5x + 0.2y = 0.8 0.3x - 0.1y = 0.7 43. 1 2 x + 1 3 y = 49 18 1 2 x + 2y = 4 3 44. 1 5 x + 1 7 y = 12 5 1 10 x + 1 3 y = 5 6
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